This article is cited in 6 papers

Creation of soliton pairs in nonlinear media with low dissipation

D. N. Ivanychev, G. M. Fraiman

Institute of Applied Physics, Russian Academy of Sciences

Abstract: Two weakly interacting KdV solitons in the presence of low viscosity are considered. A model describing their interaction in terms of a slow change of parameters of the two-soliton solution of the KdV equation under perturbation is proposed. It is shown that the inverse scattering method as well as Whitham's method lead to the same system of reduced equations. The found solutions are in good correspondence with the results of numerical calculations. The main result is a creation of a bound quasistationary pair of solitons with their successive dissipation. Although both creation and dissipation processes are due to the low viscosity, the former one is essentially faster.

Received: 26.07.1996

DOI: 10.4213/tmf966

 English version: Theoretical and Mathematical Physics, 1997, 110:2, 199–213

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